I was playing wired as my batts were almost dead and today went back to playing wireless, I noticed something that I thought i would not that it was slightly slower just a tiny bit but enough that I noticed after a few games. Tbh I thought maybe my sensitivity setting might have been changed nope it was because I was used to playing wired crazy.
Being a competitive game that Halo 5 is where having even a slight edge matters am now on going to be playing wired.
I just wanted to contribute to the topic by stating that I play wired 99% of the time with an Elite controller and I have, also, noticed this slight bit of extra latency when switching to wireless (on a full battery charge). I am hyper-sensitive to minor fluctuations in latency - likely, due to the fact that I've been playing FPS titles regularly since they became a thing for most of my life -many hrs per day, everyday.. (I'm 34 now).
The extra latency associated with wireless mode is definitely there, however, most people wouldn't even notice it and, tbh, as much as it bothers me to feel an extra frame or two of input delay, it shouldn't directly hinder my performance or anyone else's, however, (for me) it has the potential to do so, indirectly, (mentally) because the thought of this has the tendency to distract me during a gaming session.
Wireless latency will be greater than wired latency, however, on a full battery charge the difference is negligible due to the fact that the XB1 controller handles wireless mode much more efficiently than legacy devices such as X360 controllers & current-gen alternatives such as the PS Dualshock controllers (which are horrid, imo). Furthermore, as battery power lessens, the latency will increase to some degree.